Two people who were previously unaccounted for after the partial collapse of an Iowa apartment building Sunday have been found safe, Davenport police said Thursday. But three others who lived in the crash zone remain missing.

Rescuers have been trying to find Branden Colvin Sr., Ryan Hitchcock and Daniel Prien, whose apartments were in the massive section of the building that disintegrated, police said.

Now, city officials and the families of the missing men are grappling with what should happen next.

If rescuers try to re-enter, the rest of the building could topple and crush them.

"It's dangerous, and it's shifting," Mayor Mike Matson said Thursday.

But plans to demolish the Davenport building -- originally scheduled for Tuesday morning -- are now on hold.

"We're not anywhere near doing that right now," the mayor said. "We are working on a timeline. We are reaching out to experts that have particular expertise in taking it down (in) a dignified and respectful way."

A son wants to 'run in there right now'

Branden Colvin Jr. has been sleeping on the pavement outside the partially collapsed building, where his father may be trapped in the rubble.

The 18-year-old should be getting ready for his high school graduation Saturday. But he refuses to leave the scene -- even as officials warn the rest of the building could come crashing down at any time.

"If they told me I could, I'll run in there right now," Colvin told CNN, fighting back tears. "I haven't slept. I have been out here three days, at night, all night, just waiting for anything."

The teen said he's desperate to hear the voice of his father, Branden Colvin Sr.

"I love how much he talks. Before, it was annoying. But now, I just miss him," he said.

While no deaths were reported, eight people were rescued from the building within a day of the collapse, officials said. By Monday afternoon, the city said rescue efforts had turned into a recovery operation, and the building was expected to be demolished Tuesday morning.

But those demolition plans were scrapped after a ninth survivor was unexpectedly rescued from an apartment late Monday.

"That right there is an indicator that we need to go up there (again)," Davenport Fire Marshal Jim Morris said Tuesday.

But each time rescue crews went into the structure, the building shifted, Morris said. And a massive weight load on what's left of the roof -- including air conditioning units and utility equipment -- intensifies the risk of total collapse, potentially crushing rescue crews and anyone else who may be inside.

Now, the families of some of the missing are at odds about what should happen next.

The family of Ryan Hitchcock has already accepted the likelihood that their loved one is gone and supports the city's plans to carefully take down the rest of the building to prevent further harm, relative Amy Anderson said.

"Ryan wouldn't want anyone else to put their lives at risk," Anderson said at a news conference Tuesday.

"I don't discount that he could be trapped under there miraculously," she said. "But we don't want to see any more families lose their lives or anybody else be injured in trying to remove that rubble and have anything fall."

After days of using dogs, drones, thermal imaging and other tools, the odds of finding more survivors appear slim.

"We are partnering with other entities as well as our department to remove any possible human remains with dignity," said Morris, the Davenport fire marshal.

And the way the building partially collapsed "reduces the chances that there will be spaces -- what we call void spaces -- large spaces where people can survive," said Larry Sandhaas, a structural engineer hired by the city to assess the building.

But Colvin's family hasn't given up and urged officials to keep searching.

"You know there are people still unaccounted for, but you want to tear down the building. What sense does that make?" Colvin's cousin Preston McDowell told CNN. "They're not giving us any answers. I just don't get it."

The missing man's son said he's not sure if he'll be able to walk across the stage at graduation Saturday.

"We had finals this week, Tuesday, and I tried to go to school. As soon as I walked in, I just broke down, and I was just crying," the younger Colvin said. "So, I don't know if I am going to be able to go to my graduation."